Question: A circle has a radius of $5$. An arc in this circle has a central angle of $240^\circ$. What is the length of the arc? ${10\pi}$ ${240^\circ}$ $\color{#DF0030}{\dfrac{20}{3}\pi}$ ${5}$
Answer: First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (5) = 10\pi$ The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{240^\circ}{360^\circ} = \dfrac{s}{10\pi}$ $\dfrac{2}{3} = \dfrac{s}{10\pi}$ $\dfrac{2}{3} \times 10\pi = s$ $\dfrac{20}{3}\pi = s$